Solitonic Solutions of the Su(2) Nambu-Jona-Lasinio Model with Vector Mesons

Abstract

The large Nc expansion has been a useful device in order to treat QCD in the non-perturbative regime. In the leading order, this expansion allows to interpret baryons as solitons of a yet unknown effective mesonic action1. This motivates the use of specific effective models exhibiting one of the most salient features of QCD, dynamical chiral symmetry breaking. The Nambu—Jona-Lasinio model2 incorporates this feature and thus has been studied intensively in recent years in the vacuum-, meson- and baryon-sector3,4. In the large Nc. The generalization of the NJL model including vector mesons allows to describe not only a wider meson spectroscopy, but also to implement important phenomenological principles such as Sakurai’s Universality and Vector Meson Dominance realized through Current-Field Identities7,8,9. In addition, almost all heuristic attempts to relate this model to QCD require the inclusion of vector mesons10,11 In previous works the role of the vector mesons in the solitonic sector of the NJL model has been partially analysed, either in a non chirally symmetric version including the ρ meson only12, or in chirally invariant forms with ω13 or ρ and A114,15 mesons. In all cases, the free parameters were fixed via a heat kernel expansion up to second order. Of course, this corresponds to neglect the momentum dependence of the meson propagators. Due to the smallness of the pion mass this is an accurate procedure in the σ, π case. However, vector mesons masses are considerably higher and therefore the validity of such an approximation is at least questionable. As it has been pointed out in Ref. 16, a full momentum dependent treatment of mesonic correlation functions of the bosonized NJL model leads to considerable differences as compared to a heat kernel expansion up to second order. Among others, the corresponding cut-off gets reduced substantially.